Piezoelectric MEMS microphone

ABSTRACT

A piezoelectric MEMS microphone comprising a multi-layer sensor that includes at least one piezoelectric layer between two electrode layers, with the sensor being dimensioned such that it provides a near maximized ratio of output energy to sensor area, as determined by an optimization parameter that accounts for input pressure, bandwidth, and characteristics of the piezoelectric and electrode materials. The sensor can be formed from single or stacked cantilevered beams separated from each other by a small gap, or can be a stress-relieved diaphragm that is formed by deposition onto a silicon substrate, with the diaphragm then being stress relieved by substantial detachment of the diaphragm from the substrate, and then followed by reattachment of the now stress relieved diaphragm.

CROSS-REFERENCE TO RELATED APPLICATION

This application claims the benefit of U.S. Provisional Application No.61/076,928, filed Jun. 30, 2008, the entire contents of which are herebyincorporated by reference.

TECHNICAL FIELD

This invention relates generally to piezoelectric microphones and, inparticular, to piezoelectric MEMS microphones and design techniques forconstructing such microphones to meet the requirements of a particularend use application.

BACKGROUND OF THE INVENTION

The rise of microelectromechanical systems (MEMS) technology has enabledthe development of acoustic transducers such as microphones usingsilicon-wafer deposition techniques. Microphones fabricated this way arecommonly referred to as MEMS microphones and can be made in variousforms such as capacitive microphones or piezoelectric microphones usinga material such as PZT, ZnO, PVDF, PMN-PT, or AlN. MEMS capacitivemicrophones and electret condenser microphones (ECMs) are used inconsumer electronics and have an advantage over typical piezoelectricMEMS microphones in that they have greater sensitivity and lower noisefloors. However, each of these more ubiquitous technologies has its owndisadvantages. For standard ECMs, they typically cannot be mounted to aprinted circuit board using the typical lead-free solder processingcommonly used on all other microchips attached to the board. MEMScapacitive microphones, which are often used in cell phones, arerelatively expensive due at least in part to the use of anapplication-specific integrated circuit (ASIC) that provides readoutcircuitry for the microphone. MEMS capacitive microphones also have asmaller dynamic range than typical piezoelectric MEMS microphones.

The noise floors of various known piezoelectric and capacitive MEMSmicrophones are shown in FIG. 1. As indicated by the two encircledgroups of microphones, capacitive MEMS microphones (the lower group)generally have a noise floor that is about 20 dB lower than similarlysized piezoelectric MEMS microphones.

Known piezoelectric MEMS microphones have been made either ascantilevered beams or as a diaphragm, and these microphones include bothelectrodes and the piezoelectric material along with a structuralmaterial such as Parylene or silicon that is used as a diaphragm or beamsubstrate material. An advantage of Parylene for cantilever designs isthat it is can be used to increase the thickness of the beam which bothincreases the bandwidth of the beam (for a fixed length) and increasesthe distance from the neutral axis of the piezoelectric material, whichseemingly increases sensitivity. For example, beam substrates of about20 μm are known, see Ledermann [15]. For piezoelectric MEMS microphonesthat utilize a Parylene diaphragm, thinner layers have been used. See,for example, U.S. Pat. No. 6,857,501 and Niu [10]. Note that the variousreferences made herein to other authors are references to literature andjournal articles identified at the end of this description and areprovided only for non-essential subject matter in support of or asbackground for some of the teachings herein. Each of the referencedworks are hereby incorporated by reference.

SUMMARY OF THE INVENTION

In accordance with one aspect of the invention, there is provided apiezoelectric MEMS microphone, comprising a substrate and a multi-layeracoustic sensor having at least three layers that includes a firstelectrode layer, an intermediate layer of piezoelectric materialdeposited over the first electrode layer, and a second electrode layerdeposited over the piezoelectric material. The sensor is dimensionedsuch that the ratio of output energy to sensor area for the multi-layersensor is at least 10% of the maximum ratio obtainable for a given inputpressure, bandwidth, and piezoelectric material.

In accordance with another aspect of the invention, there is provided apiezoelectric MEMS microphone, comprising a substrate and a multi-layeracoustic sensor having at least three layers that includes a firstelectrode layer, an intermediate layer of piezoelectric materialdeposited over the first electrode layer, and a second electrode layerdeposited over the piezoelectric material. The sensor is dimensionedsuch that an optimization parameter calculated according to the equation

${{Optimization}\mspace{14mu}{Parameter}} = {\frac{V_{out}^{2}C}{P^{2}{{A\tan}(\delta)}} \cdot f_{res}^{2}}$is at least 10% of the maximum obtainable optimization parameter for thesensor, where V_(out) is output voltage of the sensor, C is thecapacitance of the sensor, P is the input pressure, A is the sensorarea, tan(δ) is dielectric loss angle of the sensor at the sensor'sfirst resonant frequency, and f_(res) is the first resonant frequency.

In accordance with another aspect of the invention, there is provided apiezoelectric MEMS microphone, comprising a silicon substrate and aplurality of beams each supported at one end by the substrate such thateach beam is cantilevered and extends between a fixed end and a freeend. Each beam comprises a deposited layer of electrode material and adeposited layer of piezoelectric material overlying the electrodematerial. At least some of the beams are stacked such that the stackedbeams include alternative layers of deposited electrode material anddeposited piezoelectric material with no additional layers therebetween.

In accordance with yet another aspect of the invention, there isprovided a piezoelectric MEMS microphone, comprising a substrate and astress-relieved diaphragm suspended above the substrate. The diaphragmcomprises a multi-layer acoustic sensor having at least three layersincluding a first electrode layer, an intermediate layer ofpiezoelectric material deposited over the first electrode layer, and asecond electrode layer deposited over the piezoelectric material. Thestress relieved diaphragm can be obtained in any suitable manner, suchas for example, by detaching it from the substrate about substantiallyall of its periphery and allowing it to expand or contract as needed torelieve residual stress. The diaphragm can then be reattached to thesubstrate about its periphery by any suitable technique.

BRIEF DESCRIPTION OF THE DRAWINGS

One or more preferred exemplary embodiments of the invention willhereinafter be described in conjunction with the appended drawings,wherein like designations denote like elements, and wherein:

FIG. 1 is a plot of noise levels versus sensor area for various knownMEMS microphones;

FIG. 2 is a plot depicting the influence of diaphragm residual stress onoutput energy of a piezoelectric MEMS microphone;

FIG. 3 a is a top view of a beam cantilever piezoelectric MEMSmicrophone sensor constructed in accordance with one aspect of theinvention;

FIG. 3 b depicts a cross-sectional view of two pairs of facing beamsfrom the microphone sensor of FIG. 3 a;

FIG. 3 c shows alternating beam layers and their dimensions for use inmodeling the behavior of the stacked beams shown in FIG. 3 b;

FIG. 4 depicts a schematic of the microphone of FIG. 3 a connected to anamplifying circuit, showing impedance modeling for the circuit;

FIG. 5 is a plot of typical noise curves for a piezoelectric acousticsensor;

FIG. 6 depicts the impact of beam taper on the output energy of thesensor of FIG. 3 a;

FIG. 7 depicts the impact of including one or more Paralyene layersshowing the impact of layer thickness on the output energy of apiezoelectric MEMS microphone sensor;

FIG. 8 is a plot showing how different electrode materials affect theenergy output of a piezoelectric MEMS microphone sensor;

FIGS. 9 a-9 d depict the processing steps used to make the sensor ofFIG. 3 b;

FIG. 10 is a microscope picture of a fabricated sensor of FIG. 3 a;

FIG. 11 is a picture of a piezoelectric MEMS microphone using the sensorof FIG. 3 a;

FIG. 12 shows plots of the frequency response of the microphone of FIG.11;

FIG. 13 is a plot of the beam deflection profile of the microphone ofFIG. 11;

FIG. 14 is a plot of the measured and predicted sensitivities and noisefloors for the microphone of FIG. 11;

FIG. 15 is a plot of the normalized output energy as a function ofelectrode length for a cantilever beam of the type shown in FIG. 3 a;

FIG. 16 is a plot showing the degradation of the d₃₃ coefficient fromthe piezoelectric coupling coefficient matrix for the AlN piezoelectricmaterial;

FIG. 17 is a plot showing the degradation of the dielectric loss angletan(δ);

FIG. 18 is a plot showing Mo resistivity as a function of the electrodelayer thickness;

FIG. 19 is a plot of the relationship between piezoelectric layerthickness and the d₃₁ coefficient from the piezoelectric couplingcoefficient matrix for the AlN piezoelectric material;

FIG. 20 is a plot showing the dielectric loss angle as a function of AlNlayer thickness;

FIG. 21 depicts the calculated optimization parameter as a function ofMo bottom electrode layer thickness for a single (non-stacked)cantilever beam;

FIG. 22 depicts the calculated optimization parameter as a function ofAlN intermediate layer thickness for a single (non-stacked) cantileverbeam;

FIG. 23 depicts the calculated optimization parameter as a function ofMo upper electrode layer thickness for a single (non-stacked) cantileverbeam;

FIG. 24 depicts the calculated optimization parameter as a function ofMo bottom and top electrode layer thickness for a five layer (stacked)cantilever beam;

FIG. 25 depicts the calculated optimization parameter as a function ofAlN intermediate layer thickness for a five layer (stacked) cantileverbeam;

FIG. 26 depicts the calculated optimization parameter as a function ofMo middle electrode layer thickness for a five layer (stacked)cantilever beam;

FIG. 27 a is a top view of a diaphragm piezoelectric MEMS microphonesensor constructed in accordance with one aspect of the invention;

FIG. 27 b is a partial cross-sectional view taken along the B-B line ofFIG. 27 a; and

FIG. 28 is a plot of expected noise floors for piezoelectric MEMSmicrophones constructed in accordance with the invention, showing howthey compare to known piezoelectric and capacitive MEMS microphones.

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

The description that follows is directed to various embodiments of apiezoelectric MEMS microphone that meets an optimization criteria whichcan be determined in one or more of the different manners describedbelow.

Typical piezoelectric MEMS microphones are designed so as to optimizesensitivity of the microphone, and this is at least partiallyresponsible for the increased noise floors noted above for thesedevices. As described below, by optimizing the ratio of output energy tosensor area for a given input pressure, bandwidth, and piezoelectricmaterial, a piezoelectric MEMS microphone can be constructed that hassufficient sensitivity for typical applications along with a noise floorsimilar to that of capacitive MEMS microphones. This approach is validfor films of good quality. However, as the film is reduced in thickness,the film quality will degrade. This factor can be accounted for with analternative approach described herein which utilizes a calculatedoptimization parameter that is still a ratio of sensor energy to area,but also includes the pressure, natural frequency (which limits thebandwidth), and the loss angle of the device. By adding these parametersinto the calculated ratio, this alternative approach accounts for theeffects of these parameters, rather than considering them as constants.Thus, as will be appreciated by those skilled in the art, the followingembodiments are described in conjunction with two different usableapproaches for determining an optimal or near-optimal sensor design—1) astraight calculation of output energy to sensor area ratio for a given(constant) input pressure, bandwidth and piezoelectric material and 2) acalculation of an optimization parameter that accounts for the pressure,natural frequency (which limits the bandwidth), and the loss angle ofthe device. This optimization parameter can be determined using theequation:

${{Optimization}\mspace{14mu}{Parameter}} = {\frac{V_{out}^{2}C}{P^{2}{{A\tan}(\delta)}} \cdot f_{res}^{2}}$where V_(out) is the output voltage, C is the device capacitance, P isthe input pressure, A is the sensor area, tan(δ) is the dielectric lossangle or dissipation factor of the microphone at the first resonantfrequency, and f_(res) is the first resonant frequency of the device.The use of this optimization parameter and the material characteristicsand device geometry used in calculating this parameter will be describedfarther below. When the optimal film thicknesses are compared to thefilm properties plotted in FIGS. 18, 19, and 20 that are describedfurther below, it is clear that most optimal film thicknesses havevalues such that they have nearly the properties of a thick film. Forthese films, optimization of the calculated energy to sensor area alonemay be suitable without accounting for changes in electrode and/orpiezoelectric properties. However, making the films substantiallythinner than the optimal thicknesses can cause a large relative changein material properties, in which case use of the optimization parametermay be more suitable in determining sensor optimization.

There are at least two aspects of more conventional piezoelectric MEMSmicrophone designs that have typically kept these prior designs fromachieving this optimization. A first is the use of sensor structures,such as diaphragms, that have their stiffness dominated by tension. Forpiezoelectric MEMS microphone fabricated on a silicon wafer substrate,this tension is the result of residual stress left on each layer afterdeposition. This effect leads to a reduction in normalized outputenergy, one of the elements of the optimization parameter, as can beseen in FIG. 2. This figure shows how residual stress reduces thenormalized output energy of a diaphragm with two 1 μm aluminum nitride(AlN) layers and three 100 nm molybdenum (Mo) layers with 20 kHzresonant frequency. Stresses as low as 1 MPa, a stress level difficultto achieve, reduces the normalized output energy of this diaphragm by20%, reducing the optimization parameter by 20% as well. A secondproblem with prior designs that have kept them from approachingoptimization of the relationship noted above is that these designs havenot utilized optimal or near-optimal device geometries. Thus, forexample, with cantilevered designs for which device residual stress isnot a significant factor (due to the device being released from itssubstrate when forming the cantilever), the combination of layerthickness, layer order, beam shape, and even beam spacing to adjacentbeams, make up the overall device geometry for which optimization isdesired.

In accordance with the disclosed embodiments, these problems can beaddressed in one or more ways. For cantilevers where device residualstress is not problematic, this can be done by utilizing a microphonedesign that achieves at least 10% of the maximum ratio obtainable ofoutput energy to sensor area for a given input pressure, bandwidth, andpiezoelectric material. As used herein, the “maximum ratio obtainable”for a given sensor design can be determined using an output energycalculation along with sensor area, or can be determined using theoptimization parameter equation given above along with available (albeitsometimes varying) values and equations for the various parameters usedin the optimization equation. In this latter approach, suitable sensordesigns can be obtained for which the calculated optimization parameteris at least 10% of the maximum obtainable optimization parameter for thesensor. Other ways of determining the maximum ratio obtainable arepossible, such as by repeated experimental determination or by usingother optimization equations or techniques that are either now known orlater developed. To achieve the desired level of 10% or more of themaximum optimization attainable, it has been determined through modelingand subsequent prototype testing that it is beneficial to make thesensor nearly as thin as possible and employing it in a topology inwhich multiple beams are either stacked to increase output or are builtas individual beams with a thin (˜1 μm) Parylene layer located centrallybetween the electrode and crystalline layers. In either approach, aplurality of beams can be produced that are then wired in a combinationof series and parallel connections to obtain a desired combination ofdevice capacitance and sensitivity for any given application. Fordiaphragms, an improved piezoelectric MEMS microphone can be built usinga stress-relieved diaphragm, in which the piezoelectric sensor is madeby deposition on a silicon-based substrate, then released from thesubstrate to permit expansion or contraction of the released membrane torelieve any residual stress, and then re-attached in any suitablemanner. This technique could work for a diaphragm with any combinationof clamped, pinned, or free perimeter conditions. Use of theoptimization calculation above can also be used in making the diaphragmpiezoelectric MEMS microphone to provide enhanced microphone sensitivityand noise performance. These cantilever and diaphragm designs provideuseful operation of the device for many applications, and designs forwhich the calculated optimization parameter is above 10% of optimal canprovide enhanced operation that provides good sensitivity with noisefloors per unit area that are on par with or exceeding that ofcapacitive MEMS microphones.

The following embodiments provide exemplary designs using theabove-described techniques, and the discussion that follows providesadditional mathematical and fabrication details concerning how thevarious embodiments can be designed, implemented, and checked foroptimization of the ratio noted above. Although optimization of theenergy to sensor area ratio and, in particular, use of the optimizationparameter is helpful in determining part or all of the sensor geometry,doing so is not necessary, as it is sufficient if the resultingmicrophone, however designed, meets the optimization criteria describedherein.

Single and Stacked Beam Cantilevers

FIG. 3 a depicts a beam cantilevered piezoelectric MEMS microphone 30that comprises a multi-layer acoustic sensor having a plurality offingered beams 32, each cantilevered at one of the two left and rightsides 34, 36 of the microphone such the free ends of each facing pair ofbeams 32 are separated by a small gap 38 that can be formed using knownMEMS manufacturing technology. Preferably, this gap is no greater than 3μm, but can be larger depending on the design. For most applications, agap of no greater than 10 μm can be used. A similar gap 40 can be usedbetween adjacent (side-by-side) beams. Cantilevering of the beams 32reduces the influence of material residual stress on the devicebandwidth. Each beam 32 shown in FIG. 3 a can be a single, isolated beamthat is interconnected with the other beams to produce the overallmicrophone 30 having the desired capacitance and sensitivitycharacteristics. Alternatively, as shown in FIG. 3 b, each beam 32 showncan be the upper beam of a stacked set of two or more beams formed byalternating layers of electrode and piezoelectric material. In FIG. 3 b,there are five alternating layers, although it will be appreciated that,for a stacked beam configuration, additional layers could be used. Thesebeams are constructed without any other layers or materials such thatthe beams comprise only electrode and piezoelectric layers. In theexample shown, the electrode material is molybdenum and thepiezoelectric material is aluminum nitride; however, it will beappreciated that any suitable conductive material can be used for theelectrodes (e.g., titanium) and any suitable piezoelectric material canbe used, such as PZT, ZnO, or others.

The beams 32 can have dimensions determined according to the designmethodology described below to provide a desirable set ofcharacteristics. For some embodiments, the piezoelectric layer can beunder 1 μm, and more preferably, about 0.5 μm, although again this willvary based on a number of factors, including other beam dimensions,materials, etc. For most applications, the beam thickness, and thus thepiezoelectric thickness, will be less than 2 μm, but can go as high as 8μm depending upon the particular application involved. Preferably, thepiezoelectric layer thickness is made as thin as possible whilemaintaining good piezoelectric film quality. For example, the layer canbe made as thin as the available manufacturing technology makes possibleas long as it has sufficient thickness to exhibit a sufficientpiezoelectric effect for the particular application involved. The beamlength should be related to the thickness, as indicated in the designdescription below. The electrode layer can vary as well, but preferablyis on the order of 0.2 μm or less. Preferably, the base end of the beamsare supported with a minimal amount of area to help minimize theresulting capacitance.

The MEMS microphone 30 has several advantageous features, any one ormore of which can be achieved using the design methodologies describedherein. These features include:

-   -   1. A maximized or near-maximized ratio of output energy to        sensor area for a given bandwidth, pressure, and piezoelectric        material.    -   2. The ability to design in a desired combination of sensor        capacitance and sensitivity which is achieved by a combination        of series and parallel connections between the individual beams.        This can be done without impacting the overall output energy of        the microphone and without impacting the input referred        piezoelectric noise.    -   3. The use of adjacent beams separated by a small air gap that        provides a high impedance to higher frequency sounds, thereby        enabling the device to be designed with a lower frequency        cutoff. As noted above, this can be done by keeping the space        between adjacent beams (i.e., the gap between the facing ends of        the beams and/or the gap between the adjacent sides of the        beams) to within 10 μm and preferably within 3 μm. These gaps        can be designed as discussed in Ledermann [15].    -   4. The use of stacked beams formed only of alternating layers of        electrode and piezoelectric material.

The design of the cantilever microphone 30 for any particularapplication can be carried out using the design methodology describedbelow. This methodology was developed based on mathematical modeling ofthe beams that was primarily done analytically and verifiedexperimentally. The sensitivity of a single beam has been determined bystarting with equation (20) of Krommer [1] and then determining the beamequation to be:

${{\rho\;{A(x)}\frac{\partial^{2}{w\left( {x,t} \right)}}{\partial t^{2}}} + {\frac{\partial^{2}\;}{\partial x^{2}}\left( {\sum\limits_{l = 1}^{N}\;{M\left( {x,t} \right)}} \right)}} = {f\left( {x,t} \right)}$where${\sum\limits_{l = 1}^{N}\;{M\left( {x,t} \right)}} = \begin{matrix}{{- \frac{b}{3}}\frac{\partial^{2}w}{\partial x^{2}}{\sum\limits_{l = 1}^{N}\;{\frac{1}{S_{11l}}\left( {1 + \frac{d_{31l}^{2}}{{ɛ_{33l}s_{11l}} - d_{31l}^{2}}} \right)}}} \\{\left\lbrack {\left( {z_{l} - z_{o}} \right)^{3} - \left( {z_{l - 1} - z_{o}} \right)^{3}} \right\rbrack +} \\{\frac{b}{2}{\sum\limits_{l = 1}^{N}\;{\frac{1}{s_{11l}}d_{31l}V_{l}\frac{\left( {z_{l} - z_{o}} \right)^{2} - \left( {z_{l - 1} - z_{o}} \right)^{2}}{z_{l} - z_{l - 1}}}}}\end{matrix}$ρ is the density averaged through the thickness, A is thecross-sectional area, w is the beam deflection, t is time, x is thedistance along the beam, M is the beam bending moment, f is the forceper unit width, b is the beam width, N is the number of layers l, s isthe elastic material compliance, d is a piezoelectric couplingcoefficient, ∈ is the electric permittivity, z is the height from thebottom of the beam as seen in FIG. 3 c, and V is the voltage across thelayer. z₀ would be the neutral axis if the beam had no piezoelectricmaterial and can be computed:

$z_{o} = {\frac{1}{2}{\frac{\sum\limits_{l = 1}^{N}\;{\frac{1}{s_{11l}}\left( {z_{l}^{2} - z_{l - 1}^{2}} \right)}}{\sum\limits_{l = 1}^{N}\;{\frac{1}{s_{11l}}\left( {z_{l} - z_{l - 1}} \right)}}.}}$

The boundary conditions for the beam equation are:

w − 0@x = 0 $\frac{\partial w}{\partial x} = {{0@x} = 0}$${{\sum\limits_{l = 1}^{N}\;{M\left( {x,t} \right)}} = {{0@x} = L}},{and}$${\frac{\partial}{\partial x}{\sum\limits_{l = 1}^{N}\;{M\left( {x,t} \right)}}} = {{0@x} = {L.}}$

The voltage, V, in the moment equation can be determined by extendingthe method of Irschik [2] to multiple layers resulting in:

$V_{l} = {- {\frac{d_{31\; l}}{{S_{11\; l}ɛ_{33\; l}} - d_{31\; l}^{2}}\left\lbrack {{{\frac{1}{2}\left\lbrack {\left( {z_{l} - z_{o}} \right)^{2} - \left( {z_{l - 1} - z_{o}} \right)^{2}} \right\rbrack}\frac{1}{L}\frac{\partial{w\left( {x = L} \right)}}{\partial x}} + \frac{\sum\limits_{l = 1}^{N}\;{\frac{1}{S_{11\; l}}d_{31\; l}{V_{l}\left( {z_{l} - z_{l - 1}} \right)}}}{\sum\limits_{l = 1}^{N}{\frac{1}{S_{11\; l}}\left( {z_{l} - z_{l - 1}} \right)}}} \right\rbrack}}$The capacitance of a layer is given by:

$C_{l} = {\frac{ɛ_{33\; l}{bL}}{z_{l} - z_{l - 1}}.}$The output energy of a layer is calculated by multiplying the square ofthe layer voltage by the layer capacitance:OutputEnergy_(l)=V_(l) ²C_(l)The device output energy (referred to as the output energy) will be thesum of the output energy of each layer provided that the beams 32 arewired in any combination of series or parallel that preserves thisproduct. In designing and constructing the microphone 30, the parametersof the beam layup (e.g., layer height and length) can be selected suchthat the ratio of this output energy to the sensor area is maximized fora given input pressure, bandwidth, and piezoelectric material. Thisratio is:

$\frac{OutputEnergy}{SensorArea}.$Here, sensor area refers to the total chip surface area comprisingpiezoelectric beams. Preferably, the microphone 30 is designed andconstructed to achieve as close to the maximum achievable value aspossible. However, owing to a variety of reasons (e.g., cost ofconstruction), designs of even as low as 10% of the optimal energy tosensor area ratios may be acceptable for certain applications.

It is advantageous to maximize this ratio term for two reasons. First,the output energy remains constant when wiring the beams 32 in series orparallel (allowing the microphone to be matched to a specific circuit).This has been pointed out in the work of Ried [9]. Second, the inputreferred piezoelectric noise remains constant when wiring the beams inseries or parallel. Because both of these characteristics remainconstant, maximizing this ratio can be used as a way to optimize thedesign.

The foregoing equations can be used with beams of arbitrary width andsolved numerically to determine the sensitivity of the beam. For widerbeams (plates), a simple substitution has been suggested by DeVoe [3] toturn the uniaxial stress assumption used above to a plane stressassumption. This substitution is

${\frac{1}{s_{11}} = \frac{1}{s_{11}\left( {1 - \upsilon^{2}} \right)}},\mspace{11mu}{{{and}\mspace{14mu} d_{31}} = {{d_{31}\left( {1 + \upsilon} \right)}.}}$

However, Elka [4] has shown that the initial uniaxial strain assumptiongives better results when compared to a 3D analytical model or a 3Dfinite element model. If it is assumed that the beam is of constantwidth, the equations simplify significantly and can be solvedanalytically. The assumption of small piezoelectric coupling fromTiersten [5] results in further simplifications. These equations can beused to determine the voltage developed by a specific beam and extendedto determine the voltage developed by several beams, therefore givingthe sensitivity of the piezoelectric microphone. Because beam densityhas been included in these equations, they can also be used to estimatethe bandwidth of the microphone. These equations assume voltage sensingwill be used and that the output of the beams is going into a highimpedance input. Similar equations could be derived if charge sensing isassumed. These equations are also laid out in the works of Krommer [1]and Irschik [2]. For those skilled in the art, these equations could beused in the same manner as those given above to determine an optimizeddevice utilizing charge amplification electronics.

The noise floor (minimum detectable signal) of the piezoelectricmicrophone 30 is limited fundamentally by the dielectric loss angle ofthe material as described by Levinzon [6]. This piezoelectric noise isthermal noise caused by the resistance of the film expressed as:

${\frac{\overset{\_}{v_{n}^{2}}}{\Delta\; f} = {4\;{kT}\frac{1}{\omega\; C\;{\tan(\delta)}}}},$where v_(n) is the noise spectral density, Δf is the bandwidth, k isBoltzmann's constant, T is the temperature, ω is the radian frequency, Cis the sensor capacitance, and tan(δ) is the tangent of the dielectricloss angle of the material. This determines the output voltage noise ofa given beam 32 or combination of beams. Other noise sources such asmechanical thermal noise from the beams, radiation impedance of thebeams, and 1/f noise do not dominate the noise of the microphone.

Another significant source of noise is the noise of the accompanyingelectronics. The amplification electronics could be anything rangingfrom a charge amplifier to an integrated circuit for voltageamplification. The demonstrated device uses a junction field effecttransistor (JFET) in a common source amplifier with a load resistor of2.2 kΩ for amplification because these transistors have relatively lownoise, are small, inexpensive, and relatively simple to model. The JFETnoise can be modeled as shown by Levinzon [7]. At low frequencies, thethermal noise of the resistor R_(b), shown in FIG. 4, dominates thecircuit. A pole is formed at the frequency ω=1/(R_(b)∥R_(p)·C) whereR_(p) is the resistance of the piezoelectric layer obtained from tan(δ).When R_(b) dominates the resistance, a larger capacitance, C, moves thepole to a lower frequency and therefore further attenuates the thermalnoise. A typical noise curve for a piezoelectric sensor connected to aJFET is shown in FIG. 5.

The dynamic range of the microphone 30 exceeds the requirements for mostapplications and will typically be limited by the electronics to whichit is connected. The microphone 30 itself consumes no power so the totalpower consumption is dependent on that of the amplification circuitry.The area of the microphone is determined by the size and number of beamsused and can be traded off with noise floor, sensitivity, and bandwidth.

The sensitivity of this microphone 30 to other parameters such asvibration and temperature has also been investigated. The sensitivity tovibration is related to the material density and thickness as given by:

$\frac{acceleration}{pressure} = {\frac{1}{\sum\limits_{l = 1}^{N}\;{\rho_{l}h_{l}}}.}$

These models were put into Matlab™ and an optimization was performed.The optimization was intended to give a bandwidth in the audible range,a low noise floor, and an area similar to that of commercial MEMSmicrophones.

Because this device 30 uses multiple beams 32, they can be connected ineither series or parallel but the output energy, the product V²C,remains constant for a given acoustic pressure as noted by Ried [9]. Themethod by which these beams are connected illustrates the trade-offbetween sensitivity and noise. If they are all connected in series, thismaximizes sensitivity but the sensor capacitance, C, will be very small.If a JFET is used for amplification, this will increase the frequency ofthe pole filtering the noise and the resulting noise will increase. Ingeneral, a small capacitance will be detrimental because the inputcapacitance to the electronics will act as a capacitive divider andreduce the signal. If all the beams are connected in parallel, thisresults in the minimum sensitivity but maximum sensor capacitance. Anoptimal capacitance, usually between the two limiting cases discussedabove (all parallel v. all series), can be identified to minimize theinput referred noise of the system when using a JFET.

Thus, as will be appreciated by those skilled in the art, area can betraded off with sensitivity and noise floor. More beams consume morearea but result in a larger V²C product. Bandwidth can also be tradedoff with noise floor, sensitivity, and area. Longer beams consume morearea but give a larger V²C product for a given area because they aremore compliant. These longer beams have a lower natural frequency and,therefore, a lower bandwidth.

There are other design/construction factors that influence microphoneoutput. As shown in FIG. 6, beams having a width that is tapered towardtheir free ends can provide a greater V²C output energy. The peak valueof this is at a beam base to tip ratio of about 0.33. Also, for at leastsingle (non-stacked) beams, a layer of Parylene interposed between theelectrode and piezoelectric can provide a better V²C output. Inparticular, after modeling the beam, FIG. 7 was generated to determinethe advantage/disadvantage of an intermediate layer of Parylene. Thisfigure shows that a thin layer of Parylene does slightly enhance the V²Cproduct of a constant area/constant bandwidth group of beams. This thinlayer was not used in the test devices because the Parylene may havehigher surface roughness leading to a reduction in film quality of thetop AlN layer. Because the top layer of AlN would likely be useless, theParylene would need to double the V²C product to be beneficial . . .which it does not. Thus, it may be desirable to limit the use ofParylene to microphone structures using on single (non-stacked) beams.Suitable materials other than Parylene that have a low modulus ofelasticity and low density can be used as well.

After modeling and optimizing the device in Matlab™, devices werefabricated. Rectangular beams (as opposed to tapered beams) were builtfor the purpose of simpler fabrication and testing. The beams were builtwith a 200 nm Mo, 500 nm AlN, 200 nm Mo, 500 nm AlN, 200 nm Mo materialstack because this combination gives relatively high sensitivity and lownoise.

AlN was selected as the piezoelectric material because it gives equal orsuperior performance compared to other common MEMS piezoelectricmaterials such as ZnO and PZT but is more CMOS compatible than either ofthose two materials. It can be difficult to identify the optimalpiezoelectric material because device performance will depend uponseveral material parameters such as d₃₁, tan(δ), electric permittivity,s, and ρ. These properties depend upon material composition, depositionpower/pressure/temperature, substrate roughness and crystal structure,material thickness, etc. In addition to material deposition variability,it can be difficult to find a source that provides all the necessaryinformation for a complete material comparison as the quoted values forthese parameters can vary substantially, more so for PZT than AlNbecause PZT has more variation in composition and orientation. Using thebest values from the literature [11]-[14] to evaluate both AlN and PZT,they seem to have approximately equal potential for a successful device,although PZT does typically result in a higher sensitivity which couldbe possibly beneficial depending upon the microphone application. AlNparameters in the literature seemed to be more consistent and AlN and Moare also already used in commercial FBAR processes so fabrications withthese materials can more easily be transitioned to a commercial device.Mo was selected because high quality AlN has been deposited on Mo andbecause it worked with the rest of the processing steps. FIG. 8 showshow different electrode materials affect the V²C product. The bestmaterials for this application are those with a low density and lowstiffness. Titanium (Ti), therefore works better than Mo but was notused because of compatibility issues with other processing steps. Thethicknesses of the layers were selected because these were the thinnestthat could be reasonably deposited with good quality. The modelsindicate that thinner layers would be beneficial but were not attemptedin the fabrication.

The processing of the device is shown in FIGS. 9 a-9 d. First, a 200 nmlayer of SiO₂ was deposited as an etch stop for the DRIE etch. Then a200 nm layer of Mo was deposited, patterned, and etched with dilute AquaRegia (9H₂O:1HNO₃:3HCL). Next, a 500 nm layer of AlN followed by a 200nm layer of Mo was deposited, patterned, and etched with dilute AquaRegia for the Mo and hot (85 C)H₃PO₄ for the AlN. Then another 500 nmAlN and 200 nm Mo were deposited, patterned, and etched. All AlNdepositions were performed at UC Berkeley by Harmonic Devices. DuringAlN deposition, residual stress was monitored in an attempt to limitbeam curvature. Following these etches, both sides of the wafer werecovered with 6 μm of SiO₂ and the back side was patterned and etched forthe DRIE etch to release the beams. Next, the wafer was etched from theback side in an STS DRIE tool. The individual die were then diced with adicing saw and the SiO₂ was removed in 5:1 BHF. Several steps could beimproved upon, most notably, the length of the beams could be more wellcontrolled if an anisotropic silicon etch were used to etch the backcavity and an etch stop was implanted into the silicon under the beams.Some designs utilized an additional metallization step before DRIE toconnect the beams in different combinations of series or parallel andreduce stray capacitance but these devices were not used in this initialproof of concept. A microscope picture of the device can be seen in FIG.10.

After fabricating the devices, they were packaged in a transistoroutline (TO) can as seen in FIG. 11 and wire bonded to a JFET to bufferthe signal. This can be done as indicated in FIG. 4 with the gate inputof the JFET being connected to the sensor electrodes such that signalsreceived from the electrodes are amplified by the transistor. A hole wasdrilled in the TO can below the microphone in order to give opticalaccess to the beams and measure their deflection. This hole also allowsthe size of the back cavity to be adjusted, as the size of the backcavity will determine the low end of the microphone bandwidth. Themicrophone was then placed in a plane wave tube next to a referencemicrophone (Larsen Davis model 2520) and the frequency response wasmeasured using a LabView A/D card and software. This can be seen in FIG.12. The d₃₁ coefficient was measured by actuating the beams andmeasuring the beam curvature with a laser vibrometer. The beamdeflection profile can be seen in FIG. 13.

The natural frequency of the beams was determined by measuring thefrequency response of the beams to actuation. Another parameter thatinfluences the microphone performance is the dielectric loss angletan(δ) of the microphone. This has been measured with both customcircuitry in conjunction with LabView™ software and with an AgilentModel 4284A Precision LCR meter.

For this initial test, only the top layer of AlN was connected to theJFET and only on one side of the beams, thereby resulting in a noisefloor 3 dB higher than would be expected if the entire microphone wereconnected to the JFET. The beams were drawn to be 356 μm but the DRIEetched further than expected, resulting in a natural frequency ofapproximately 11 kHz. This would suggest the beam length is actuallyapproximately 400 μm. The d₃₁ coefficient was measured as 1.68×10⁻¹²N/C. This value is about 65% of the best values quoted in theliterature. The d₃₁ coefficient has been shown to correlate with theX-ray diffraction rocking curve FWHM which, for this layer, is about 2.6degrees while the best reported are around 1 degree. This value islikely higher than others because the layer is only 0.5 μm thick and ontop of other layers. Tan(δ) was measured as 0.04 at 1 kHz. Theliterature typically gives tan(δ) in the range of 0.001 to 0.002 so thisvalue is more than an order of magnitude higher than those typicallyquoted. It was determined that this higher than expected tan(δ) is dueto some residual material left after etching the AlN with H₃PO₄. Aftersome investigation, it was found that the tan(δ) can be reduced bycleaning with Acetone while in an ultrasound bath and heating on a hotplate. The devices with a lower tan(δ) will result in microphones with alower noise floor.

With the measured d₃₁ coefficient and tan(δ) and using the lengthderived from the natural frequency measurement, the microphone modelmatches the measured performance quite well. The sensitivity, shown inFIG. 14, is measured as 0.52 mV/Pa out of the JFET common sourceamplifier with a 2.2 kOhm load resistor. This equates to a raw outputsensitivity of 0.17 mV/Pa for the piezoelectric microphone. The modelpredicts an output sensitivity of 0.18 mV/Pa. The measured inputreferred noise floor for the device is 58.2 dBA while the model predictsan input referred noise floor of 57.3 dBA. FIG. 14 shows the measuredand predicted sensitivities and noise floors. The first peak in themeasured frequency response is caused by the natural frequency of thebeams across from those used in the measurement. They are not exactlythe same length due to a non-uniformity in the DRIE etch.

In the cantilevered beam designs described above, optimization of theoutput energy to sensor area ratio was determined based on a given inputpressure, bandwidth, and piezoelectric material. However, theseconstraints can be taken into account in the design or analysis of apiezoelectric MEMS microphone. In particular, using the optimizationparameter equation:

${{Optimization}\mspace{14mu}{Parameter}} = {\frac{V_{out}^{2}C}{P^{2}A\;{\tan(\delta)}} \cdot f_{res}^{2}}$the input pressure can be accounted for by the pressure P term, thebandwidth by the f_(res) term, and the characteristics of thepiezoelectric material and the electrode by the dielectric loss angletan(δ). Thus, where a given set of these input constraints is not used,the output energy to sensor area ratio can be optimized by maximizingthe optimization parameter equation given above to take those otherfactors into account.

As one example, consider again a piezoelectric MEMS microphone thatutilizes a rectangular cantilevered beam having one AlN piezoelectriclayer and two Mo electrode layers. For a cantilever, the normalizedoutput energy can be plotted as a function of electrode length as shownin FIG. 15. As the normalized output energy per unit area increases, sowill the optimization parameter so the electrode will go from the baseof the beam to roughly 50% the length of the beam.

When using aluminum nitride as a piezoelectric material, smallpiezoelectric coupling can be assumed. This assumption simplifies theexpression for output voltage from that given above for V₁ to

$V_{out} = {- \frac{{PbL}^{2}d_{31}Z_{Q}}{12\;{EI}\;\eta\; s_{11}}}$where P is the pressure amplitude, b is the cantilever width, L is thecantilever length, d₃₁ is the 31 term of the piezoelectric couplingcoefficient matrix, η is the electric permittivity of the piezoelectricmaterial, s₁₁ is the 11 term of the compliance matrix,Z_(Q)=(Z_(k)−zn)²−(z_(k-1)−zn)², where zn is the beam neutral axis, thesubscript k refers to the layer and, in this case, refers to thepiezoelectric layer, and EI is the beam bending rigidity given as

${EI} = {\frac{b}{3}{\sum\limits_{k = 1}^{N}\;{\frac{1}{s_{k}}Z_{Ck}}}}$where Z_(Ck)=(Z_(k)−zn)³−(Z_(k-1)−zn)³ and zn is given as

${zn} = {\frac{1}{2}{\frac{\sum\limits_{k = 1}^{N}\;{\frac{1}{s_{k}}\left( {z_{k}^{2} - z_{k - 1}^{2}} \right)}}{\sum\limits_{k = 1}^{N}\frac{h_{k}}{s_{k}}}.}}$The capacitance is approximately

$C = \frac{\eta\; A_{e}}{h_{p}}$where A_(e) is the area covered by the electrode and h_(p) is the heightof the piezoelectric layer. The first resonant frequency isapproximately

$f_{res} = {\frac{1.875^{2}}{2\pi\; L^{2}}{\sqrt{\frac{EI}{b{\sum\limits_{k = 1}^{N}{\rho_{k}h_{k}}}}}.}}$The dielectric loss angle of the microphone is a function of the lossesin the piezoelectric material itself as well as the losses in theelectrodes. This can be approximated as

${\tan(\delta)}_{mic} = {{\tan(\delta)}_{p} + \frac{2\eta_{p}\omega\; L^{2}}{3\sigma_{e}h_{e}h_{p}}}$where the subscripts, p and e, refer to the piezoelectric material andelectrode material respectively, σ is the material conductivity, ω isthe radian frequency, and L is the length of the electrode.By combining these equations, assuming the length of the electrode isequal to the length of the cantilever beam, the optimization parametercan be calculated as

${OptimizationParameter} = {\frac{{bd}_{31\; p}^{\;_{2}}Z_{Q_{p}}^{2}\sigma_{e}h_{e}h_{p}}{\begin{matrix}{{3\;{EIh}_{p}^{2}\eta_{p}s_{11\; p}^{2}\sigma_{e}h_{e}\;{\tan(\delta)}_{p}{\sum\limits_{i = 1}^{N}{\rho_{i}h_{i}}}} +} \\{{2 \cdot 1.875^{2}}\eta_{p}\sqrt{\frac{EI}{b{\sum\limits_{i = 1}^{N}{\rho_{i}h_{i}}}}}}\end{matrix}}.}$

Using this equation and thickness independent material properties, theoptimization would lead to zero thickness layers and an infiniteoptimization parameter. As the molybdenum layer gets thin, however, itsconductivity decreases. Also, very thin AlN tends to have a reducedpiezoelectric coupling coefficient and a large loss angle. For thisreason, these relationships must be included in the optimization.

The d₃₁ data can be extracted by assuming that the d₃₁ coefficientdegrades at the same rate as the d₃₃ coefficient. Plots of d₃₃ andtan(δ) degradation are given in Martin [16] and are shown in FIGS. 16and 17, respectively. Alternatively, the dependence of d₃₁ on thicknesscould be determined experimentally.

The Mo conductivity will also change as the thickness is decreased. Thedependence of Mo thickness with resistivity can be obtained using themodel of Namba [17] to determine this relationship for modelingpurposes. Using this model, a mean free path of 140 nm, P=Q=0, and anRMS surface roughness of 0.5 nm, the relationship between Mo thicknessand resistivity can be determined. The assumed relationships between Moresistivity and Mo thickness, between d₃₁ and AlN thickness, and betweenloss angle and AlN thickness are shown in respective FIGS. 18-20. Usingthe optimization parameter equation and the data from the plots above,the ideal thicknesses for a three layer device are shown in Table 1below.

TABLE 1 Layer Thickness Molybdenum #1   9 nm Aluminum Nitride 1.5 μmMolybdenum #2 1.1 μm

For added accuracy, the fluid loading of air above and below a 1 mm×1 mmdiaphragm has been added to the density summation. The natural frequencyequation can then be used to calculate the length of the beam. For anatural frequency of 20 kHz, the beam will be 374 μm long. The plots ofFIGS. 21-23 show the effect of changing any layer thickness on theoptimization parameter. Small relative changes do not greatly affect thevalue of the optimization parameter except in the case of the bottom Mothickness. For this reason, it may be wise to use a more conservativebottom Mo thickness such as 20 nm. Of course, even more conservativevalues that maintain the optimization parameter above 10% of its maximumobtainable value can be used; thus, electrode thicknesses of 50 nm, 100nm or more can be used since, as shown in FIGS. 18-20 the optimizationparameter, particularly of the bottom electrode, does not decrease toosubstantially with thicknesses in this range. If the desired sensor areais roughly 1 mm×1 mm, this beam can be made to be 1 mm wide and three ofthem can be placed end to end.

This same approach can be used for the stacked beam configuration shownin FIG. 3 b of five alternating layers of electrodes and piezoelectricmaterial. Calculated optimal values that maximize the optimizationparameter are given below in Table 2.

TABLE 2 Layer Thickness Molybdenum #1 10 nm Aluminum Nitride #1 1.5 μm Molybdenum #2 10 nm Aluminum Nitride #2 1.5 μm  Molybdenum #3 10 nm

The natural frequency equation can then be used to calculate the lengthof the beam. For a natural frequency of 20 kHz, the beam will be 461 μm.The plots of FIGS. 24-26 show the effect of changing any layer thicknesson the optimization parameter. Again, these plots show that theelectrode layer can be increased significantly to, e.g., 20, 50, 100 nmor more without suffering too great a reduction in the calculated outputvoltage to sensor area ratio, and that the middle electrode can bevaried between 5 nm and 1 μm without reducing the ratio to below 10% ofits maximum obtainable value.

Diaphragm Designs

As noted above, rather than a cantilever beam structure, a stressrelieved diaphragm design can also provide a good combination ofsensitivity and low noise floor. Turning now to FIGS. 27 a and 27 b,there is shown a piezoelectric MEMS microphone 50 comprising amulti-layer acoustic sensor in the form of a stress-relieved diaphragm52 suspended above a silicon substrate 54. In this embodiment, onlythree layers are used, upper and lower Mo electrode layers, and anintermediate layer of AlN piezoelectric material. However, it will beappreciated that Parylene and other material layers can also be used,and that the diaphragm can have multiple piezoelectric layers such asdiscussed above in connection with the stacked beam cantileverconfigurations. Although the illustrated embodiment includes only threelayers, the upper and lower electrode layers are patterned to eachdefine two independent electrodes. In particular, the first (lower)electrode layer includes a central electrode 56 and an outer ring shapedelectrode 58 that surrounds the central electrode 56. The second (upper)electrode layer shown in FIG. 27 a also includes a central electrode 57and an outer ring shaped electrode 59 that surrounds the centralelectrode 57. From the perspective of the top view shown in FIG. 27 a,both the central electrode 57 and outer ring electrode 59 areco-extensive with their associated lower central electrode 56 and ringelectrode 58, respectively. As will be appreciated, the centralelectrodes 56, 57 form a first piezoelectric sensing element and theouter ring electrodes 58, 59 form a second piezoelectric sensingelement. By maintaining the electrodes electrically isolated from eachother, they can be wired together as desired. Since the outer ringpiezoelectric sensing element is strained in the opposite direction asthe central sensing element, the charge produced on these electrodes bythe piezoelectric effect will be of opposite polarity, such that theycan be added together by connecting central electrode 56 to outer ringelectrode 59 and by connecting central electrode 57 to outer ringelectrode 58. The signals from the sensor can be amplified by connectionto a transistor, op-amp or other suitable circuitry in a similar mannerto that discussed above in connection with the cantilever embodiments.

To obtain the stress relieved diaphragm 52, the layers can be formed bydeposition onto a silicon wafer or other suitable substrate 54, with thediaphragm then being micromachined or otherwise processed tosubstantially detach it from the substrate so that the layers can expandor contract as necessary to relieve any residual stress. As shown inFIG. 27 a, one way to accomplish this is to use springs 60 to hold thediaphragm 52 in place while it is otherwise released from the substrate54. Once it is stress relieved, the diaphragm 52 can then be reattachedto the substrate 54 about its periphery by any suitable technique, suchas via electrostatic clamping. The springs 60 are created by etchingthrough the AlN to form the border and then undercutting the springs byremoving the material below them. The diaphragm 52 is connected to thesubstrate 54 in the bottom right corner in an area that is used forelectrode leads. The springs in the remaining three corners are thenfixed to the substrate 54 at one end and to the diaphragm 52 at theother. After undercutting the springs, the diaphragm 52 can bereattached to the substrate 54 by holding the bottom, outer electrode 58at ground and applying a voltage bias to the substrate. Thus, thediaphragm 52 has a first portion of its perimeter (at the bottom right)that is attached to the substrate 54 as a direct deposition of at leastone of the layers onto the substrate, and has a second portion of theperimeter attached to the substrate by separate adhesion of the secondportion onto the substrate. It also is connected to the substrate 54 atthe other corners by thin interconnections of one or more of the layersthat act as the springs 60. Electrical connection to the central andouter ring electrodes can be by way of conductive traces 62 that extendacross the piezoelectric layer at the bottom right corner where thediaphragm 52 remains connected to the substrate 54. The optimal layerthicknesses and sizes can be obtained by following the same procedure asabove for the cantilever designs. A reasonable estimate of layerthicknesses can be found by using the same parameters given above;alternatively, a diaphragm model could be used for a more complete andaccurate optimization.

Additional Observations

The fabricated device shows that the models are accurate and only thematerial and processing needs to be improved. When processing anddeposition techniques allow for better material properties to beachieved, the performance will match that shown in FIG. 28. This figureindicates the performance that one could expect for the designed andfabricated devices using a JFET common source amplifier with highquality material parameters. This indicates that this design for apiezoelectric microphone can achieve a noise floor on par with welloptimized capacitive microphones. Some parameters such as sensitivityand power consumption are not included in the FIG. 28 plot because theseparameters are not as significantly interrelated as those given in thefigure. The plus signs in the figure indicate piezoelectric microphonesand the circles indicate capacitive microphones. Piezoelectricmicrophones typically have lower sensitivity than capacitivemicrophones, but this can be corrected by using an application specificintegrated circuit (ASIC) to amplify the signal, as is often used incapacitive microphones. Although this figure assumes high qualitypiezoelectric material, it does not take into account the improvementsthat are possible with the use of a better electrode material, taperedbeams, or a thin compliant layer in the middle of the beam. This alsoassumes a JFET is being used for amplification, thus limiting the noisefloor. An ASIC could have a lower noise floor and improve theperformance of the microphone even further. This also assumes a tan(δ)of 0.001 but it has been shown that tan(δ) can be reduced below thisvalue with proper annealing.

A piezoelectric MEMS microphone constructed as described above couldhave commercial potential competing with electret condenser microphones(ECMs) and MEMS capacitive microphones used in consumer electronics. Thedesign offers performance on par with ECMs and MEMS capacitivemicrophones but offers advantages over each. First, standard ECMs cannotbe mounted to a printed circuit board using the typical lead-free solderprocessing used on all other microchips. This means that they must bespecially attached either by hand or in a more expensive and lessreliable socket. The previously described piezoelectric microphone canwithstand high temperatures and therefore can be mounted using standardtechniques. This piezoelectric microphone is also smaller than ECMs,allowing for a smaller overall electronic device. MEMS capacitivemicrophones also have these advantages and they have, therefore, beenused in cell phones since 2003. MEMS capacitive microphones, however,are more expensive than ECMs due, in large part, to the applicationspecific integrated circuit (ASIC) used to provide readout circuitry tothese microphones. This is a much more expensive part than the JFET usedin ECMs. The piezoelectric MEMS microphone described here can beamplified with a single JFET, therefore, creating a lower costmicrophone with all the advantages of the MEMS capacitive microphone.

Apart from use as an audio microphone, the device can be used for otherapplications such as for ultrasonic detection, with suitable changes inthe design of the microphone structure being used to optimize it forthat application. Also, by covering the beams with an insulatingmaterial such as Parylene (e.g, about 1-2 μm), the microphone can beused as a hydrophone for underwater applications. Similarly, a Paryleneor other suitable insulating covering could be used with the diaphragmdesigns described above to construct a hydrophone, in which case thedevice would include a pressure equalization port or other means ofappropriate pressure equalization with the outside environment, as willbe known by those skilled in the art.

It is to be understood that the foregoing is a description of one ormore preferred exemplary embodiments of the invention. The invention isnot limited to the particular embodiment(s) disclosed herein, but ratheris defined solely by the claims below. Furthermore, the statementscontained in the foregoing description relate to particular embodimentsand are not to be construed as limitations on the scope of the inventionor on the definition of terms used in the claims, except where a term orphrase is expressly defined above. Various other embodiments and variouschanges and modifications to the disclosed embodiment(s) will becomeapparent to those skilled in the art. For example, although sensordesigns that provide at least 10% of the maximum ratio obtainable (ormaximum obtainable optimization parameter) are suitable for manyapplications, more preferable designs will provide at least 25% of themaximum obtainable, and even more preferable designs will provide atleast 50% of the maximum obtainable. In a highly preferred embodiment, adesign using the maximum obtainable optimization parameter can beutilized. All such other embodiments, changes, and modifications areintended to come within the scope of the appended claims.

As used in this specification and claims, the terms “for example,” “forinstance,” “such as,” and “like,” and the verbs “comprising,” “having,”“including,” and their other verb forms, when used in conjunction with alisting of one or more components or other items, are each to beconstrued as open-ended, meaning that the listing is not to beconsidered as excluding other, additional components or items. Otherterms are to be construed using their broadest reasonable meaning unlessthey are used in a context that requires a different interpretation.

REFERENCES

-   [1] Krommer, M., (2001). “On the correction of the Bernoulli-Euler    beam theory for smart piezoelectric beams.” Smart Materials and    Structures, (10), 668-680.-   [2] Irschik, H., Krommer, M., Belyaev, A. K., Schlacher, K., (1998).    “Shaping of Piezoelectric Sensors/Actuators for Vibrations of    Slender Beams: Coupled Theory and Inappropriate Shape Functions.”    Journal of Intelligent Material Systems and Structures, (9),    546-554.-   [3] DeVoe, D. L., Pisano, A. P., (1997). “Modeling and Optimal    Design of Piezoelectric Cantilever Microactuators.” Journal of    Microelectromechanical Systems, (6), 266-270.-   [4] Elka, E., Elata, D., Abramovich, H., (2004). “The    Electromechanical Response of Multilayered Piezoelectric    Structures.” Journal of Microelectromechanical Systems, (13),    332-341.-   [5] Tiersten, H. F. (1969). “Linear Piezoelectric Plate Vibrations.”    (New York: Plenum).-   [6] Levinzon, F. A., (2004). “Fundamental Noise Limit of    Piezoelectric Accelerometer.” IEEE Sensors Journal, (4), 108-111.-   [7] Levinzon, F. A., (2000). “Noise of the JFET Amplifier.” IEEE    Transactions on Circuits and Systems—I: Fundamental Theory and    Applications, (47), 981-985.-   [8] Perkins, N.C. (2001), in: S. G. Braun (Ed.), Nonlinear Systems,    Overview, “Encyclopedia of Vibrations.” Academic Press, 944-951.-   [9] Ried, R. P., Kim, E. S., Hong, D. M., Muller, R. S., (1993).    “Piezoelectric Microphone with On-Chip CMOS Circuits.” Journal of    Microelectromechanical Systems, (2), 111-120.-   [10] Niu, M. N., Kim, E. S., (2003). “Piezoelectric Bimorph    Microphone Built on Micromachined Parylene Diaphragm.” Journal of    Microelectromechanical Systems, (12), 892-898.-   [11] Trolier-McKinstry, S., Muralt, P., (2004). “Thin Film    Piezoelectrics for MEMS.” Journal of Electroceramics, (12), 7-17.-   [12] Tsubouchi, K., Mikoshiba, N., (1985).    “Zero-Temperature-Coefficient SAW Devices on AlN Epitaxial Thin    Films.” IEEE Transactions on Sonics and Ultrasonics, (SU-32),    634-644.-   [13] Dubois, M. A., Muralt, P., (1999). “Properties of aluminum    nitride thin films for piezoelectric transducers and microwave    filter applications.” Applied Physics Letters, (74), 3032-3034.-   [14] Hooker, M. W., (1998). “Properties of PZT-Based Piezoelectric    Ceramics Between −150 and 250° C.” NASA Report: NASA/CR-1998-208708.-   [15] Ledermann, N., Muralt, P., Baborowski, J., Forster, M.,    Pellaux, J.-P., “Piezoelectric Pb(Zrx, Ti1-x)O3 thin film cantilever    and bridge acoustic sensors for miniaturized photoacoustic gas    detectors.” J. Micromech. Microeng. 14 (2004) 1650-1658.-   [16] Martin, F., Muralt, P., Dubois, M. A., Pezous, A., (2004).    “Thickness dependence of the properties of highly c-axis textured    AlN thin films.” J. Vac. Sci. Technol. A, Vol. 22, No. 2, 361-365.-   [17] Namba, Y., (1970). Japan J. Appl Phys. (9), 1326-1329.

The invention claimed is:
 1. A piezoelectric MEMS microphone,comprising: a substrate; and a multi-layer acoustic sensor comprising atleast three layers including a first electrode layer, an intermediatelayer of piezoelectric material deposited over said first electrodelayer, and a second electrode layer deposited over said piezoelectricmaterial; wherein said sensor is dimensioned such that an optimizationparameter calculated according to the equation${{Optimization}\mspace{14mu}{Parameter}} = {\frac{V_{out}^{2}C}{P^{2}A\;{\tan(\delta)}} \cdot f_{res}^{2}}$is at least 10% of the maximum obtainable optimization parameter for thesensor, where V_(out) is output voltage of the sensor, C is thecapacitance of the sensor, P is the input pressure, A is the sensorarea, tan(δ) is dielectric loss angle of the sensor at the sensor'sfirst resonant frequency, and f_(res) is the first resonant frequency;wherein said sensor comprises a plurality of beams each supported at oneend by said substrate such that each beam is cantilevered and extendsbetween a fixed end and a free end, each beam comprising said electrodeand intermediate layers; and wherein at least two of said beams arepositioned such that free ends of each beam face one another and areseparated by a gap of no greater than 3 μm.
 2. A piezoelectric MEMSmicrophone, comprising: a substrate; and a multi-layer acoustic sensorcomprising at least three layers including a first electrode layer, anintermediate layer of piezoelectric material deposited over said firstelectrode layer, and a second electrode layer deposited over saidpiezoelectric material; wherein said sensor is dimensioned such that anoptimization parameter calculated according to the equation${{Optimization}\mspace{14mu}{Parameter}} = {\frac{V_{out}^{2}C}{P^{2}A\;{\tan(\delta)}} \cdot f_{res}^{2}}$is at least 10% of the maximum obtainable optimization parameter for thesensor, where V_(out) is output voltage of the sensor, C is thecapacitance of the sensor, P is the input pressure, A is the sensorarea, tan(δ) is dielectric loss angle of the sensor at the sensor'sfirst resonant frequency, and f_(res) is the first resonant frequency;wherein said sensor comprises a plurality of beams each supported at oneend by said substrate such that each beam is cantilevered and extendsbetween a fixed end and a free end, each beam comprising said electrodeand intermediate layers; and wherein adjacent beams are separated by agap that is no greater than 10 μm.
 3. A piezoelectric MEMS microphone,comprising: a substrate; and a multilayer acoustic sensor comprising aplurality of cantilevered beams, each beam comprising a first electrodelayer, an intermediate layer of piezoelectric material deposited oversaid first electrode layer, and a second electrode layer deposited oversaid piezoelectric material, wherein each beam is supported at a fixedend by said substrate and extends between said fixed end and a free end,and at least two of said free ends are separated by a gap and face oneanother across said gap, wherein adjacent beams are separated by a gapthat is no greater than 10 microns.
 4. A piezoelectric MEMS microphoneas defined in claim 3, wherein said sensor is dimensioned such that theratio of output energy to sensor area for the multi-layer sensor is atleast 10% of the maximum ratio obtainable for a given input pressure,bandwidth, and piezoelectric material.
 5. A piezoelectric MEMSmicrophone as defined in claim 3, wherein said sensor is dimensionedsuch that an optimization parameter calculated according to the equation${{Optimization}\mspace{14mu}{Parameter}} = {\frac{V_{out}^{2}C}{P^{2}A\;{\tan(\delta)}} \cdot f_{res}^{2}}$is at least 10% of the maximum obtainable optimization parameter for thesensor, where V_(out) is output voltage of the sensor, C is thecapacitance of the sensor, P is the input pressure, A is the sensorarea, tan(δ) is dielectric loss angle of the sensor at the sensor'sfirst resonant frequency, and f_(res) is the first resonant frequency.6. A piezoelectric MEMS microphone as defined in claim 3, wherein saidgap is no greater than 3 μm.